Description

A description of the problem to model and solve.

In the Traveling Salesman Problem (TSP), a route has to be found between cities in such a way that all cities are visited and the route is the shortest as possible.

A distance matrix is given as input, storing distances between each pair of cities.

Since the route should form a cycle, any city can be defined as the origin one and arrival one.

See Wikipedia for more details.

Input data

We consider here the following input (in java):

// GR17 is a set of 17 cities, from TSPLIB. The minimal tour has length 2085.
// number of cities
int C = 17;
// matrix of distances
int[][] D = new int[][]{
            {0, 633, 257, 91, 412, 150, 80, 134, 259, 505, 353, 324, 70, 211, 268, 246, 121},
            {633, 0, 390, 661, 227, 488, 572, 530, 555, 289, 282, 638, 567, 466, 420, 745, 518},
            {257, 390, 0, 228, 169, 112, 196, 154, 372, 262, 110, 437, 191, 74, 53, 472, 142},
            {91, 661, 228, 0, 383, 120, 77, 105, 175, 476, 324, 240, 27, 182, 239, 237, 84},
            {412, 227, 169, 383, 0, 267, 351, 309, 338, 196, 61, 421, 346, 243, 199, 528, 297},
            {150, 488, 112, 120, 267, 0, 63, 34, 264, 360, 208, 329, 83, 105, 123, 364, 35},
            {80, 572, 196, 77, 351, 63, 0, 29, 232, 444, 292, 297, 47, 150, 207, 332, 29},
            {134, 530, 154, 105, 309, 34, 29, 0, 249, 402, 250, 314, 68, 108, 165, 349, 36},
            {259, 555, 372, 175, 338, 264, 232, 249, 0, 495, 352, 95, 189, 326, 383, 202, 236},
            {505, 289, 262, 476, 196, 360, 444, 402, 495, 0, 154, 578, 439, 336, 240, 685, 390},
            {353, 282, 110, 324, 61, 208, 292, 250, 352, 154, 0, 435, 287, 184, 140, 542, 238},
            {324, 638, 437, 240, 421, 329, 297, 314, 95, 578, 435, 0, 254, 391, 448, 157, 301},
            {70, 567, 191, 27, 346, 83, 47, 68, 189, 439, 287, 254, 0, 145, 202, 289, 55},
            {211, 466, 74, 182, 243, 105, 150, 108, 326, 336, 184, 391, 145, 0, 57, 426, 96},
            {268, 420, 53, 239, 199, 123, 207, 165, 383, 240, 140, 448, 202, 57, 0, 483, 153},
            {246, 745, 472, 237, 528, 364, 332, 349, 202, 685, 542, 157, 289, 426, 483, 0, 336},
            {121, 518, 142, 84, 297, 35, 29, 36, 236, 390, 238, 301, 55, 96, 153, 336, 0}
    };

Last modified 03.06.2020: Add TSP (13cc948)